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【理学院讲坛】数学中心学术报告
发布时间:2019-12-18【告诉好友】 【关闭窗口】

  时间:2019年12月21日上午8:30-18:00

  地点:数统楼213

  报告一陈建清(福建师范大学)

  题目包含卷积非线性的薛定鄂方程和方程组

  摘要: 本报告首先介绍一些包含卷积非线性的薛定鄂方程解的存在性、多重性等结果;接着结合变分方法介绍单个薛定鄂方程的柯西问题解的存在性;最后介绍包含卷积非线性的薛定鄂方程组的柯西问题解的存在性。

  报告二王  俊(江苏大学)

  题目Existence and bifurcation of nontrivial solutions for the coupled nonlinear Schrodinger-Korteweg-de Vries system

  摘要In this talk, we consider the existence and bifurcation of nontrivial solutions of the nonlinear Schrodinger-Korteweg-de Vries(NLS-KdV) and Schrodinger-Korteweg-de Vries-Korteweg-de Vries(NLS-KdV-KdV) systems which arise from fluid mechanics. On the one hand, for both the three-wave system and two-wave system, the

  existence/nonexistence, continuous dependence and asymptotic behavior of positive ground state solutions are established. On the other hand, multiple positive solutions are found via a combination of Nehari manifold and bifurcation methods for the attractive interaction case.

  报告黄  锐(华南师范大学)

  题目 Stability of traveling waves for time-delayed nonlocal dispersion equation

  摘要We will talk about the stability of traveling waves for time-delayed nonlocal dispersion equation, including the monotone/non-monotone  critical/non-critical traveling waves. Some numerical simulations will be also presented to confirm our theoretical results.

  报告四:刘海东(嘉兴学院)

  题目A coupled Schrodinger system with critical exponent

  摘要

   

  

  报告陈世炳(中国科学技术大学)

  题目Free boundary in optimal transport

  摘要Free boundary arises naturally in optimal transportation. The existence, uniqueness and $C^{1,\alpha}$ regularity were studied in a seminal paper by Caffarelli and McCann. In this talk, I will discuss some recent progress on this problem. This is based on a joint work with Jiakun Liu.

  报告向长林(长江大学)

  题目Regularity theory for some higher order elliptic systems

  摘要In this talk, I will discuss a regularity problem of some higher order elliptic systems originated from geometry, including the fourth order elliptic system proposed by Lamm and RiviYre which models geometric objects such as biharmonic mappings between Riemannian manifolds. Lamm and RiviYre applied the method of conservation law to derive continuity of solutions. However, their approach is quite di_cult to be applied to higher order elliptic systems. We will introduce an elementary approach which is easy to be applied to higher order problems, and also is applicable to derie Holder continuity of solutions directly. This is a joint work with Chang-Yu Guo in EPFL.

  报告邓圣兵 (西南大学)

  题目 Bubble solutions for some Neumann problems in R^2

  摘要In this talk, I will present some results about the existence of bubble solutions for some Neumann problems in R^2, the problem has exponential nonlinratity term on the boundary condition.

  报告张建军(重庆交通大学)

  题目:Sign-changing solutions of nonlinear nonlocal problems

  摘要We are concerned with sign-changing solutions of nonlinear nonlocal elliptic problems, including Schrodinger-Poisson systems, Kirchhoff equations and gauged Schrodinger equations. By employing a novel perturbation approach and the method of invariant sets of descending flow, we prove that the problems above admit multiple sign-changing solutions.

  报告王春花(华中师范大学)

  题目Multi-peak positive solutions to a class of Kirchhoff equations

  摘要In this talk, we consider a nonlocal Kirchhoff problem. Under some mild assumptions on the function V, we obtain multi-peak solutions for  sufficiently small by Lyapunov-Schmidt reduction method. Even though many results on single peak solutions to singularly perturbed Kirchhoff problems have been derived in the literature by various methods, there exist no results on multi-peak solutions before our work, due to some difficulties caused by the nonlocal term. A remarkable new feature of this problem is that the corresponding unperturbed problem turns out to be a system of partial differential equations, but not a single Kirchhoff equation, which is quite different from most of elliptic singular perturbation problems. This is based on a joint work with Prof. S. Peng, P. Luo and C. Xiang.

      
      
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